On bilinear representations and infinite conservation laws of a nonlinear variable-coefficient equation

The KdV equation for non-uniform media with relaxation effects has extensive applications in mathematics and physics. Satsuma (1976) [20] and Hirota (1979) [21] once investigated its algebraic properties. In the paper, we shall generalize it a more general integrable equation with variable coefficients and further discuss the corresponding bilinear representation, Bäcklund transformation, Lax pair and infinite conservation laws by making use of the Bell polynomials.